I need help with this math problem

Question

Write an exponential function in the form y = a * b ^ x that goes through points (0, 6) and (5, 6144)

Answer 1

The points you were given are values of "x" and "y", so plug them into y = ab^x like this:

1) 6 = ab⁰

2) 6144 = ab⁵

In equation 1), b⁰ = 1 (anything to the zero power is 1). That mean a = 6. Plugging in a = 6 into equation 2) we get:

6144 = (6)b⁵

6144/6 = b⁵

1024 = b⁵

b = 5th root(1024) = 4

So the exponential equation (plugging in a = 6 and b = 4) is y = 6(4^x)